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Pappus and Guldinus's theorems are powerful mathematical principles that are used for finding the surface area and volume of composite shapes. For example, consider a cylindrical storage tank with a conical top. Finding the surface area or volume can be challenging for such complex shapes. These theorems are particularly useful in calculating the volume and surface area of such systems. Here, the cylindrical storage tank with a conical top can be broken down into two simple shapes: a...
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Generating Strictly Controlled Stimuli for Figure Recognition Experiments
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The World Is Not a Theorem.

Stuart Kauffman1, Andrea Roli2,3

  • 1Institute for Systems Biology, Seattle, WA 98109, USA.

Entropy (Basel, Switzerland)
|November 27, 2021
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Summary
This summary is machine-generated.

Affordances drive biosphere evolution by offering opportunities for adaptation. However, set theory cannot formalize affordances, preventing a mathematical model for evolutionary dynamics.

Keywords:
affordancediachronic evolution of the biosphereincompletenessset theory

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Area of Science:

  • Evolutionary Biology
  • Theoretical Biology
  • Ecology

Background:

  • The biosphere evolves through the generation of new life forms and functions.
  • Organisms adapt to environmental opportunities, a process fueled by heritable variation and selection.
  • Affordances, or the opportunities offered by the environment, are crucial for adaptation.

Purpose of the Study:

  • To investigate the role of affordances in biosphere evolution.
  • To determine if affordances can be formalized using set theory.
  • To assess the possibility of a set-based mathematical theory for diachronic biosphere evolution.

Main Methods:

  • Conceptual analysis of affordances in evolutionary processes.
  • Critique of applying set theory to biological affordances.
  • Argument against a set-based mathematical framework for evolutionary dynamics.

Main Results:

  • Affordances are integral to the exploitation of environmental opportunities for adaptation.
  • Set theory is inadequate for formalizing the concept of affordances.
  • A set-based mathematical theory cannot be developed to explain the diachronic evolution of the biosphere.

Conclusions:

  • The dynamic and context-dependent nature of affordances resists formalization by static set theory.
  • Understanding biosphere evolution requires frameworks beyond set-based mathematical models.
  • Future research should explore alternative theoretical approaches to model evolutionary dynamics driven by affordances.